Probability Seminar: Recurrence of the Simple Random Walk Path

  • Date: 11/25/2009
Ori Gurel-Gurevich (Microsoft)

University of British Columbia


A simple random walk (SRW) on a graph is a Markov chain whose state
space is the vertex set and the next state distribution is uniform
among the neighbors of the current state. A graph is called recurrent
if a SRW on it returns to the starting vertex with probability 1, and
called transient otherwise. The path of a walk on a graph is simply the
set of edges this walk has traversed. Our main result is that the path
of a SRW on any graph is a recurrent graph. The proof uses the
electrical network interpretation of random walks. We will give a
sketch of the proof, including the necessary background, and discuss
related questions and conjectures.


3:00pm - 4:00pm, WMAX 110.